Limits & Continuity Questions and Answers

Match each graph with its equation O a r 9 4 cos 0 b r 4 cos 0 c r 2 4 cos 0 d r 4 4 cos 8 e r 6 4 cos 0

Rewrite the Cartesian equation a r 0 Enter theta for 8 if needed 3 as a polar equation

Convert the Cartesian coordinate 1 6 to polar coordinates 0 0 2 r Enter exact value 0

vertical line test Function Function 00 2 OYes 4 Yes 2 2 4 y O ONO Graph 4 2 No 4 1 O Yes 8 64 24y Yes 1 2 Graph 5 4 O NO 2 2 4 6 8 No 6 4 Yes THT 0 2 y 2 4 Graph 6 OYes 2 4 No No 6

Using the guidelines of curve sketching sketch the graph of f x 1 x 1

The logistic model P t 91 9991 1 0 0407 e 0 1976t represents the percentage of households that do not own a personal computer t years since 1983 Complete parts a d a Evaluate and interpret P 0 Evaluate P 0 P 0 Round to one decimal place as needed

The function f is defined as foll f x x 4 Find f 121 and f 31 f 121 0 f 31

The function h is defined as follows h x Find h 3 x 2 14x 45 x 9 wwwwww

r 2 5r 2 2x 1 x 4 10 f x a 4 pts Find the r and y intercepts Identify the multiplicities of the zeros i e z intercepts b 4 pts Identify the vertical asymptotes with multiplicity and the horizontal or slant asymptotes c 4 pts Sketch the graph without a calculator based on the above answers Clearly label all intercepts and asymptotes Use technology to create a graph and compare it to what you drew

Fill in the table using this function rule f x x 3 Simplify your answers as much as possible Click Not a real number if applicable X 1 0 16 0 0 0

Fill in the table using this function rule f x x 5 Simplify your answers as much as possible Click Not a real number if applicable f x 0 1 X 4 0 4 100 7 0 9 0 Not a real number

Miguel wants to save 600 to buy a TV He saves 17 each week The amount A in dollars that he still needs after w weeks is given by the following function A w 600 17w Answer the following questions a If Miguel still needs 294 how many weeks has he been saving weeks b How much money does Miguel still need after 7 weeks

Use a graph to find an approximate solution to the equation 2 6191 ex 1 10 Round to the nearest hundredth

The functions fand g are defined as follows g x 3x 3 f x 2x 3x Find f 4 and g 2 Simplify your answers as much as possible f 4 0 0 X

In Exercises 31 40 find the Taylor series centered at c and the interval on which the expansion is valid 31 33 34 3 1 32 f x e x c 1 f x 37 f x c 1 1 1 x c 5 f x sin x c f x 1 2 35 f x x 3x 1 36 f x x 3x 1 E G x2 C 4 2 38 f x x c 4 c 2 c 0

Function 4 Graph 1 2 Yes 4 2 2 y 2 C O NO No Graph 4 Graph 2 8 6 4 2 99 OYes 8 6 4 2 2 24 6 8 y 8 54 2 4 Graph 5 1 2 4 6 8 O No 6 8 2 4 1 Graph 3 24y Yes 2 O No Graph 6 2

The function is defined by the following rule f x 2x 5 Complete the function table X 3 0 1 3 4 f x 0 0 1 0

42 Show that for x 1 tanh x x d tanh 1 x3 3 1 18 10 x5 5

Score for Question 3 of 4 points Pre Calculus Trigonometry Graded Assignment Semester B Unit 3 Exam Part 2 3 The range of a cosecant function is 9 5 00 The equations of two consecutive asymptotes of the function are x 0 and x 2x The function is not a reflection over the x axis What is the equation of this cosecant function Answer

Orange juice a raisin bagel and a cup of coffee from Billy s Breakfast Bar cost a total of 3 00 Billy posts a notice announcing that effective the following week the price of orange juice will increase 50 and the price of bagels will increase 20 After the increase the same purchase will cost a total of 3 75 and the orange juice will cost twice as much as coffee Find the price of each item before the increase What was the cost of a glass of orange juice before the increase What was the cost of a raisin bagel before the increase What was the cost of a cup of coffee before the increase

The function h is defined by the following rule h x x 2 Complete the function table X 2 1 0 3 4 h x 0 0

Total score Score for Question 1 of 6 points 1 Consider the polar equation r 3 sin 20 Answer 0 0 a Complete the tables for the given values of 0 Round to the nearest tenth as needed b Graph the equation a r 3 sin 20 r 3 sin 20 b of 15 points 6 7 5r 5 6 0 7 6 5 4 37 3r W wt 49 3 2 50 6 5T 4 A 1 3 2 1 KIN 01 1 4 4 3 1 2 3 3 2 5 11 KIN 6 2 506 5T 3 2r 2 T 3 7 4 3 4 117 6 57 6 2 T

Ex Find the volume of the solid generated by the x axis and the line x 4 0 1 about the y x X y axis 4 the region bounded by the curve y x

Score for Question 2 of 6 points 2 Corey spies a bald eagle in a tall tree He estimates the height of the tree to be 80 feet and the angle of elevation to the bird from where he stands to be 68 The leaves on the tree make it difficult for Corey to watch the bird so he takes several steps away from the tree to get a better view He now estimates his angle of elevation to be 41 How many feet did Corey step back to gain a better view of the bird Round your answer to the nearest hundredth of a foot Answer

61 X 11 1 NMIS 2 3 4 5 648 7 IN and y t 5 0 t 8 x y 0 5 124 292 0 34 3 3 5857 1 3 6 Y 5 3 2 3 2679 2 3 26 3 2 3 5 2 2 7639 2 2 763 2 5505 3 2 5505 7 2 2254 2 2 354 2 1715 4 2 1715 4 F 2x t Label all points from table and use arrows to show direction curve follows on graph

X A 5 B 4 C 2 D 2 E 4 3 2 2 h x 5 4 C 62 The table above shows some values of the function h which is defined for all real numbers x If h is an odd function what is the value of c

Compute each of the given indefinite integrals a 8 da a 810 x db a 8 2 610 dx C C C

The logistic growth model P t 3000 1 32 47 e 0 473t represents the population in grams of a bacterium after t hours Answer parts a throught f a Determine the carrying capacity of the environment The carrying capacity of the environment is g

Let f x 2x 1 Simplify each of the following expressions f a 2a 1 f a h 2 a h 1 f a h f a 2 a h 1 2a 1 f a h f a 2 h X Make sure to expand and combine like terms Make sure to cancel out the factor of h in the denominator

ctions Course Packet on the composition of functions Let f x 2x 7 and g x 4x 4 Determine the rule for the composite functions fo g and go f fog x gof x

Packet on the composition of functions If f x 38 4 x 11 and g x 2x2 36 compute the composition fog 5 fog 5 Enter a fraction integer or exact decimal Do not approximate

Determine the range of each of the following functions Enter your answer using interval notation a Range of 2x 20 b Range of 2x 20 2x c Range of 20 11 K

Complete each of the following problems a Find all values of x such that x 4 0 Enter your answer as a comma separated list of values The order of the values does not matter b Find all values of x such that x 4 0 Enter your answer using interval notation c Find all values of x such that x 4 0 Enter your answer using interval notation

Use the table to find the instantaneous velocity of y at the specified value of x 2 x 0 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 8 8 4 Y 10 38 58 70 74 70 58 38 10

Identify the function for the given graph Answer Of x x Of x x Of x 1 X X

The variable a is jointly proportional to the cube of b and the square of c If a 367 when b 6 and c 7 what is the value of a when b 5 and c 3 Round you answer to two decimal places if necessary Answer Keypac Keyboard Shortcu

Evaluate the indefinite integral as an infinite series arcta arctan x dx 2 c C Ms

Suppose that y is proportional to the cube of x and that y 6 when x 10 What is y when x 11 Round your answer to two decimal places if necessa Answer Keyb

Pre Calculus Trigonometry Graded Assignment Score for Question 2 of 4 points 2 What are the solutions of the equation 2 sin 4x 1 on the interval 0 7 Answer

Total score Score for Question 1 of 12 points of 4 points 1 What is the exact value of sin

2 pt Use Cramer s rule to solve the system of equations 1 12 213 14 1 71 272 23 2x4 0 21212 13 2 2

1 4 26 Given the graph of f x graph y f x List the domain and range of EACH graph an list the EXACT VALUES of any invariant points 3

Pre Calculus Trigonometry Graded Assignment Semester B Unit 5 Exam Part 2 Score for Question 3 of 5 points 3 Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30 with the horizontal The ball hit her bat when the ball was 3 feet above the ground Answer a No one interferes with the ball How long does it take the ball to hit the ground Round your answer to the nearest hundredth of a second Show all your work b How far did the ball travel horizontally Use your answer from Part a in your calculations Round your answer to the nearest tenth of a foot Show all your work

3 Answer 3 Points 6 Step 2 of 2 Determine if the relation is a function If it is not identify two ordered pairs as proof Selecting an option will display any text boxes needed to complete your answer Function yes no

1 point Connie has to solve the following problem 5 boxes of cereal costs 12 50 How much will 18 boxes cost Choose EVERY proportion Connie could use to solve this problem 5 12 5 5 12 5 12 5 5 5 18 1 8 18 2 18 I 12 50

If there are 15 girls and 9 boys in an art class the ratio of girls to boys in the class is

A company produces metal slabs for industrial use The slabs come in 3 thicknesses 5in 10in and 15in The weights of each thickness for each metal are given below Metal 1 150lbs 300lbs 600lbs Metal 2 130lbs 260lbs 390lbs Metal 3 310lbs 620lbs 930lbs Metal 4 140lbs 280lbs 420lbs For which of the metals is weight NOT proportional to thickness Metal 1 Metal 4 Metal 2 Metal 3

Graph the following function and its inverse on the same Cartesian plane f x 1 x log x Use the graphing tool to graph the function Click to enlarge graph 10 B 6 4 10 2

Graph the following function Based on the graph state the domain and the range and find any intercepts f x A In x if 0 x 1 In x if x 1 16 OB The domain is x x x OB 16 Simplify your answer Use a comma to separate answers as needed OC The domain is x x Q Simplify your answer Use a comma to separate answers as needed OD The domain is the set of all real numbers What is the domain of the function Select the correct choice below and if necessary fill in the answer box es to complete your choice O A The domain is x xz X Simplify your answer Use a comma to separate answers as needed C 16 Q O Points 0 of 1 D Ay 5

16 Solve the following system of equations 3x 5y 5z 21 4x 5z 17 2x 5y 6z 16